2208.02616
Zariski Dense Orbit Conjecture on Birational Automorphisms of Projective Threefolds
Sichen Li
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the two desired reductions (Theorem 1.5) by combining an equivariant special MRC fibration with a sharp base-reduction lemma (Proposition 3.2), thereby fully handling κ(X) = −∞ and K_X ∼ 0. In contrast, the candidate solution leaves the surface-base subcase κ(Z) = 0 unresolved in the uniruled regime and only asserts that external structure theorems would complete it. Hence the model’s argument is incomplete, while the paper’s is complete (modulo clearly cited inputs).
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The core reductions (Theorem 1.5) are correct, clearly stated, and proved with appropriate, standard inputs. The treatment of the special MRC fibration and the base-reduction lemma (Proposition 3.2) elegantly closes the uniruled case. The K\_X ∼ 0 case is handled cleanly via known structure results and elementary dynamical reductions. Some minor typographical/notation issues (e.g., “surjective endomorphism” for a morphism) and a few places where assumptions could be restated for clarity are the only obstacles to immediate acceptance.